Question

Show that, for any integer n > 2, (n + 1)" - 1 is divisible by n2. (Hint: Use the Binomial Theorem.)

Answer 1

Answer:

It's true

Step-by-step explanation:

Operating the square we have:

$(n+1)^{2} -1= (n^{2} +2n+1)-1\\ n^{2} +2n+1-1= n^{2} +2n$

Here we can factorize n:

$n^{2} +2n=n*(n+2)$

The last line means our number ($(n+1)^{2} -1$) is divisible by n.

The clause of n>2 is true, but even its true for $n\geq 0$ because when n=1 the theorem means that the expression is divisible by 1, but this it's true for every integer, and for n=0 the expression will be 0 and 0 it´s divisible by 0 (Following the definition a|b if a=nb, with a, b and n integers).